Simplify. Remove all perfect squares from inside the square root. Assume $a$ is positive. $\sqrt{27a}=$
Answer: Factor $27$ and find the greatest perfect square: $27=3\cdot 3\cdot 3=3^2\cdot 3$ There are no perfect square factors of $a$. $\begin{aligned} \sqrt{27a}&=\sqrt{3^2\cdot 3a} \\\\ &=\sqrt{3^2}\cdot \sqrt{3a} \\\\ &=3\cdot \sqrt{3a} \\\\ &=3\sqrt{3a} \end{aligned}$